3-Digit Subtraction Worksheets

3-digit subtraction uses the same steps as 2-digit subtraction with one more column, and a borrow can now happen twice. The eight PDFs on this page have problems with no borrowing, mixed problems and problems that always borrow, plus grid paper, 3-digit minus 2-digit, a riddle, match-up cards and story problems. Every sheet has an answer key.

They follow standards 2.NBT.B.7 and 3.NBT.A.2 of the Common Core standards for grade 2 number and operations in base ten and the Common Core standards for grade 3 number and operations in base ten, and the notes below show the steps, how often each kind of borrow happens and other ways to find the same answer.

About these 3-digit subtraction worksheets

Three-digit subtraction uses the same steps as 2-digit subtraction with one more column. Borrowing can now happen twice: once from the tens and once from the hundreds. In 812 − 356, the ones borrow from the tens, then the tens borrow from the hundreds, giving 456.

The steps

1. Line up hundreds, tens and ones.
2. Work from right to left, borrowing whenever the top digit is too small.
3. Remember that a digit you borrowed from is now one less.
4. Check: answer + bottom number = top number.

What is on this page

• No borrowing, mixed and always borrowing: three sets that increase in difficulty.
• Grid paper: for neat columns.
• 3-digit minus 2-digit: children must line up numbers of different lengths.
• A riddle and match-up cards for review.
• Story problems with 3-digit numbers.

Problems with zeros in the top number, such as 500 − 267, have their own page: subtracting across zeros.

3-digit subtraction worksheets: what is in the set

There are 8 3-digit subtraction worksheets on this page, and every one has an answer key except for any cut-out games. There are three sets of column problems that increase in difficulty, one on grid paper, one with a 2-digit number taken from a 3-digit number, a riddle, match-up cards and story problems.

3-digit subtraction: the steps column by column

3-digit subtraction has three columns, ones, tens and hundreds, and the steps are the same as in 2-digit subtraction with regrouping. Work from right to left, borrow when the top digit is too small, and remember that a digit you borrowed from is now one less. This table shows 812 − 356, where the ones borrow from the tens and the tens then borrow from the hundreds:

The picture above shows the same trades on a place-value board. The second borrow is the one that children find hard, because the tens digit has already lent a ten to the ones and may be left with too little. In 812 − 356 the 1 ten became 0 tens, and 0 is less than 5, so the tens must borrow again. The base ten blocks tool lets children trade a flat for ten rods on the screen.

3 digit subtraction worksheets: how many borrows does a problem need?

The three sets in the 3 digit subtraction worksheets are called no borrowing, mixed and always borrowing, so it helps to know how common each kind is. This table counts every subtraction of two 3-digit numbers where the top number is the same as or bigger than the bottom number, which is 405,450 problems:

Only a third of all 3-digit subtractions need no borrowing, and more than a fifth need two. That is a much higher share of borrowing than in 2-digit subtraction, where 60% of problems need none. The table below splits the same problems by the columns that borrow, which explains why the second borrow is trickier than the first:

Ones-only and tens-only borrows are both common, and about one problem in five has both. A child who has met all four patterns has met every kind of 3-digit subtraction. The mixed worksheet contains all four.

3 digit subtraction with regrouping: the 3-digit minus 2-digit problems

3 digit subtraction with regrouping is hardest when the second number has only two digits, as in 734 − 58, because children must line up numbers of different lengths. This table shows the steps:

The hundreds column has no digit to subtract, so the 7 simply becomes 6 after lending, and the answer is 676. The most common mistake is to write the 58 under the tens and hundreds, which gives a very different answer. This table shows how far off the answer is for four problems when the second number is shifted one place to the left:

The wrong answers are hundreds too small, which is easy to see with an estimate: 734 − 58 is about 730 − 60 = 670, not 154. The hundreds tens and ones page and the grid paper sheet both help children keep the ones under the ones.

Triple digit subtraction: other ways to find the answer

Triple digit subtraction does not always need the column method. Counting up from the smaller number is quick when the two numbers are close, and rounding the second number up to a multiple of ten and adding back is quick when it ends in 8 or 9. This table shows both for six problems, next to the number of borrows in the column method:

For 812 − 356, counting up goes from 356 to 360 (4), to 400 (40), to 800 (400) and to 812 (12), a total of 456. Children who know these methods can check an answer found by columns, and the number line tool shows the same jumps. The standard 2.NBT.B.9 asks children to explain why these strategies work, using place value.

Subtraction within 1000: estimate first, then check

Subtraction within 1000 is where an estimate becomes a useful check, since a slip in one column changes the answer by 10 or 100. Round both numbers to the nearest hundred and subtract. This table shows five problems with the estimate beside the exact answer:

The estimate is never more than 100 away from the exact answer when both numbers are rounded to the nearest hundred, so an answer that is far from the estimate has an error. The estimating with rounding page explains how to round, and the rounding to the nearest 100 pages give practice. A second check is to add the answer to the number taken away:

3rd grade subtraction worksheets: where this fits

These are 3rd grade subtraction worksheets in the sense that the Common Core standard 3.NBT.A.2 asks grade 3 children to subtract within 1,000 fluently, using strategies and algorithms based on place value. In grade 2, the standard 2.NBT.B.7 asks for the same work with concrete models and drawings, so children who still need blocks can use the base ten blocks tool and move to the column method when they are ready.

Common mistakes with 3-digit subtraction

The most common mistake is to subtract the smaller digit from the bigger in each column. This table shows five mistakes, what went wrong and the fix:

3-digit subtraction word problems

Three-digit numbers come up in counts of books, seats and kilometers. Ask children to write the subtraction, to solve it in columns and to check by adding:

Games and activities for 3-digit subtraction

Children learn 3-digit subtraction best when they play with it. These games use things that are found at home or in a classroom:

• Trade a flat: build 812 with 8 flats, 1 rod and 2 cubes, trade a flat for ten rods and a rod for ten cubes, and take away 356
• Borrow bingo: call problems that borrow once or twice, and mark the answers
• Match-up cards: match 10 problems to their differences, and sort them by the number of borrows
• Beat the borrow: roll six dice, make two 3-digit numbers, and subtract the smaller from the bigger; the player with the smaller difference wins
• Counting up race: find the difference by counting up, and then check in columns
• The riddle: solve the problems and use the answers to decode a riddle

Extra support and extra challenge with 3-digit subtraction

For children who need more support: build the numbers with flats, rods and cubes first, and write each trade beside the column. Use the grid paper sheet, so that every digit has its own box, and cross out each digit you borrow from. Start with the no-borrowing set, then the set where the ones borrow, then the set where the tens borrow, before the mixed set.

For children who need more challenge: ask for the missing digit in 8☐2 − 356 = 456, for the biggest answer from two 3-digit numbers that use the digits 1 to 6 once each, and for a subtraction where both columns borrow and the answer is 456. Move on to subtracting across zeros and to 4-digit numbers.

How to tell that a child is ready to move on from 3-digit subtraction

Before moving on from 3-digit subtraction, check that the child can do all four of these things:

1. The child can say how many borrows a problem needs by looking at the digits.
2. The child borrows twice, and writes the new digits correctly.
3. The child lines up a 2-digit number under a 3-digit number.
4. The child estimates and then checks the answer by adding.

When all four are true, 3-digit subtraction is secure, so move on to subtracting across zeros, which has zeros in the top number, or to 4 and 5-digit subtraction.

A 20-minute lesson on 3-digit subtraction

A short lesson is the best way to introduce 3-digit subtraction. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where 3-digit subtraction fits across the grades

No skill stands alone. This table shows what children learn before and after 3-digit subtraction, with the standard that goes with each step:

This page is the main page for 3-digit subtraction. The whole sequence is on the subtraction worksheets page.

Helping at home with 3-digit subtraction

Parents do not need to be experts to help with 3-digit subtraction. These suggestions work well, and each takes only a few minutes:

• Use real coins: 8 dollars, 1 dime and 2 pennies, to show how to trade a dollar for ten dimes.
• Ask “how many borrows?” before each problem.
• Check every answer by adding it back.
• Use graph paper, so each digit has a box.
• Praise the estimate as much as the answer.

How to check progress in 3-digit subtraction

A teacher or parent can check progress in 3-digit subtraction with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for 3-digit subtraction

Most children need about a week of short sessions for 3-digit subtraction. This plan follows the order of the worksheets on this page:

When the plan for 3-digit subtraction is complete, move on to subtracting across zeros. The whole sequence is on the subtraction worksheets page.